A Modern Look at Freedman's Box Model

Dennis L Sun, Joseph Alfredo
2019 Technological Innovations in Statistics Education  
This paper revisits the box model, a metaphor developed by Freedman, Pisani, and Purves (1978) to explain sampling distributions and statistical inference to introductory statistics students. The basic idea is to represent all random phenomena in terms of drawing tickets at random from a box. In this way, random sampling from a population can be described in the same way as everyday phenomena, like coin tossing and card dealing. For Freedman et al. (1978) , box models were merely a thought
more » ... iment; calculations were still done using normal approximations. In this paper, we propose a modern view of the box model as a practical simulation framework for conducting inference, thus providing a bridge between the box model and simulation-based inference in the education literature. To facilitate this simulation-based approach to teaching box models, we developed an online, open-source "box model simulator" inspired by user-centered design theory to help students scaffold their knowledge. Finally, we suggest some novel ideas for using the box model to teach bootstrapping and discrete probability.
doi:10.5070/t5121044395 fatcat:7cx3eexswvcbpnplsfm5yxkzue